Solve for $x$ : $x^2 + 6x + 5 = 0$
Answer: The coefficient on the $x$ term is $6$ and the constant term is $5$ , so we need to find two numbers that add up to $6$ and multiply to $5$ The two numbers $1$ and $5$ satisfy both conditions: $ {1} + {5} = {6} $ $ {1} \times {5} = {5} $ $(x + {1}) (x + {5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x + 5) = 0$ $x + 1 = 0$ or $x + 5 = 0$ Thus, $x = -1$ and $x = -5$ are the solutions.